The use of electrical measurements in prior art downhole applications, such as logging while drilling (LWD), measurement while drilling (MWD), and wireline logging applications is well known. Such techniques may be utilized to determine a subterranean formation resistivity, which, along with formation porosity measurements, is often used to indicate the presence of hydrocarbons in the formation. For example, it is known in the art that porous formations having a high electrical resistivity often contain hydrocarbons, such as crude oil, while porous formations having a low electrical resistivity are often water saturated. It will be appreciated that the terms resistivity and conductivity are often used interchangeably in the art. Those of ordinary skill in the art will readily recognize that these quantities are reciprocals and that one may be converted to the other via simple mathematical calculations. Mention of one or the other herein is for convenience of description, and is not intended in a limiting sense.
Directional resistivity measurements are also commonly utilized to provide information about remote geological features (e.g., remote beds, bed boundaries, and/or fluid contacts) not intercepted by the measurement tool. Such information includes, for example, the distance from and direction to the remote feature. In geosteering applications, directional resistivity measurements may be utilized in making steering decisions for subsequent drilling of the borehole. For example, an essentially horizontal section of a borehole may be routed through a thin oil bearing layer. Due to the dips and faults that may occur in the various layers that make up the strata, the distance between a bed boundary and the drill bit may be subject to change during drilling. Such distance (and direction) measurements may enable the operator to adjust the drilling course so as to maintain the bit at some predetermined distance from the boundary layer. Directional resistivity measurements also enable valuable geological information to be estimated, for example, including the dip and strike angles of the boundary as well as the vertical and horizontal conductivities of the formation.
In prior art geosteering operations, steering decisions are generally made at the surface, e.g., at the rig site or at some remote location, where there is significantly greater processing capability. LWD directional resistivity data (or other downhole data) are compressed downhole and then transmitted to the surface while drilling (e.g., via conventional telemetry techniques). The transmitted data is then processed at the surface in combination with a model of the subterranean formations to determine a subsequent drilling direction (or a correction to the current drilling direction). Changes to the predetermined (preplanned) drilling direction (e.g., in the form of a corrected well path) are then transmitted from the surface to a downhole steering tool (e.g., via conventional downlinking techniques) where they are implemented.
While geosteering methods have been commercially utilized for a number of years, there remains room for improvement. For example, the viability of prior art geosteering methods is often limited by the bandwidth and accuracy of the communication channel between the bottom hole assembly (BHA) and the surface. This limitation can cause geosteering methods to be slow and somewhat unresponsive (e.g., due to the time lag associated with transmitting LWD measurements to the surface and then transmitting steering instructions or a corrected well plan from the surface to the BHA). Moreover, telemetry errors and/or the reduced accuracy that results from data compression can lead to further errors when computing the corrected well path.
One way to overcome these limitations is to process the directional resistivity data downhole. However, prior art forward modeling and inversion algorithms tend to require intensive processing capability and are therefore generally unsuitable for use with low power downhole processors. There is therefore a need in the art for a fast inversion methodology that significantly reduces processing requirements.